 Solution

ID: past-exam-of-the-topics-in-applied-mathematics-course-of-the-university-of-oxford/2007/a/2/i/solution

k_{0} s

to autocatalytic replication, substrate-enzyme binding flux

k_{1} se

, dissociation flux

k_{- 1} c

and product-formation flux

k_{2} c

. Therefore

\overset{s}{˙} = k_{0} s - k_{1} se + k_{- 1} c, \overset{c}{˙} = k_{1} se - (k_{- 1} + k_{2}) c, \overset{e}{˙} = - k_{1} se + (k_{- 1} + k_{2}) c .

Complex breakdown to product restores free enzyme but does not restore substrate. Product concentration, if required, satisfies

\overset{p}{˙} = k_{2} c

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